Nonlinear Modulational Instabililty of the Stokes Waves in 2D Full Water Waves

被引：4

作者：

Chen, Gong ^{[1
]}

Su, Qingtang ^{[2
]}

机构：

[1] Georgia Inst Technol, Sch Math, Atlanta, GA 30332 USA

[2] Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100080, Peoples R China

来源：

COMMUNICATIONS IN MATHEMATICAL PHYSICS | 2023年 / 402卷 / 02期

关键词：

FREE-BOUNDARY PROBLEM; FINITE-TIME SPLASH; WELL-POSEDNESS; FREE-SURFACE; GLOBAL-SOLUTIONS; NLS APPROXIMATION; SOBOLEV SPACES; JUSTIFICATION; EQUATION; MOTION;

D O I：

10.1007/s00220-023-04747-0

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

The well-known Stokes waves refer to periodic traveling waves under the gravity at the free surface of a two dimensional full water wave system. In this paper, we prove that small-amplitude Stokes waves with infinite depth are nonlinearly unstable under long-wave perturbations. Our approach is based on the modulational approximation of the water wave system and the instability mechanism of the focusing cubic nonlinear Schrodinger equation.

引用

页码：1345 / 1452

页数：108

共 86 条

[71]

Wang XC, 2018, COMMUN PUR APPL MATH, V71, P90, DOI 10.1002/cpa.21711

[72] NON-LINEAR DISPERSION OF WATER WAVES [J].